Question

The specific heat of steel is 420 J/(kg°C). How much energy is required to heat 1 kg of steel by 20 °C?

Answer 1

`"8400 J"`

Explanation:

The specific heat of a substance tells you how much heat is required in order to heat one unit of mass, usually `"1 g"`, of that substance by `1^@"C"`.

In this case, the specific heat of steel uses `"1 kg"` as the unit of mass, which means that the value given to you tells you how much heat is required in order to heat `"1 kg"` of steel by `1^@"C"`.

Since you have

`c = "420 J kg"^(-1)""^@"C"^(-1)`

you can say that you need `"420 J"` of heat in order to increase the temperature of `"1 kg"` of steel by `1^@"C"`.

This means that in order to increase the temperature of a given mass of steel by `20^@"C"`, you'd need

`20 color(red)(cancel(color(black)(""^@"C"))) * "420 J"/("1 kg" color(red)(cancel(color(black)(""^@"C")))) = "8400 J kg"^(-1)`

For `"1 kg"`, this gives you

`1 color(red)(cancel(color(black)("kg"))) * "8400 J"/(1color(red)(cancel(color(black)("kg")))) = color(darkgreen)(ul(color(black)("8400 J")))`

I'll leave the answer rounded to two sig figs.